Dose-response dependencies of OSL dosimeters in conventional linacs and 1.5T MR-linacs: an experimental and Monte Carlo study

Objective. This work focuses on the optically stimulated luminescence dosimetry (OSLD) dose–response characterization, with emphasis on 1.5T MR-Linacs. Approach. Throughout this study, the nanoDots OSLDs (Landauer, USA) were considered. In groups of three, the mean OSLD response was measured in a conventional linac and an MR-Linac under various irradiation conditions to investigate (i) dose–response linearity with and without the 1.5T magnetic field, (ii) signal fading rate and its dependencies, (iii) beam quality, detector orientation and dose rate dependencies in a conventional linac, (iii) potential MR imaging related effects on OSLD response and (iv) detector orientation dependence in an MR-Linac. Monte Carlo calculations were performed to further quantify angular dependence after rotating the detector around its central axis parallel to the magnetic field, and determine the magnetic field correction factors, kB,Q, for all cardinal detector orientations. Main results. OSLD dose–response supralinearity in an MR-Linac setting was found to agree within uncertainties with the corresponding one in a conventional linac, for the axial detector orientation investigated. Signal fading rate does not depend on irradiation conditions for the range of 3–30 d considered. OSLD angular (orientation) dependence is more pronounced under the presence of a magnetic field. OSLDs irradiated with and without real-time T2w MR imaging enabled during irradiation yielded the same response within uncertainties. kB,Q values were determined for all three cardinal orientations. Corrections needed reached up to 6.4%. However, if OSLDs are calibrated in the axial orientation and then irradiated in an MR-Linac placed again in the axial orientation (perpendicular to the magnetic field), then simulations suggest that kB,Q can be considered unity within uncertainties, irrespective of the incident beam angle. Significance. This work contributes towards OSLD dose–response characterization and relevant correction factors availability. OSLDs are suitable for QA checks in MR-based beam gating applications and in vivo dosimetry in MR-Linacs.


Introduction
Optically stimulated luminescence (OSL) dosimetry has been introduced in clinical practice for quality assurance (QA) in radiotherapy applications employing photon fields emitted from clinical linear accelerators (linacs) (Jursinic 2007, Kry et al 2020).As passive cumulative dosimeters and relatively small in size, OSL dosimeters (OSLDs) have been proposed for -inter alia-in vivo dosimetry procedures, surface dose measurements, treatment plan verification and small field output factor determination (Zhuang and Olch 2014, Kim et al 2020, Kry et al 2020, Lim-Reinders et al 2020, Kido et al 2023).They are based on the principle of luminescence, which involves the stimulated emission of light by an active material after it has been exposed to ionizing radiation (Yukihara and McKeever 2008).Commercially available OSLDs use either carbon-doped aluminum oxide (Al 2 O 3 :C) or beryllium oxide (BeO) as active materials, housed in a thin plastic case (McKeever and Moscovitch 2003, Pradhan et al 2008, Jahn et al 2014, Hoshida et al 2019).Cumulative energy deposited by ionizing radiation can be read-out by stimulation of light, resulting in luminescence which increases with the delivered radiation dose (McKeever and Moscovitch 2003, Akselrod et al 2006, Jursinic 2007, Yukihara and McKeever 2008, Jursinic 2010).The read-out system is portable and can be easily installed in a clinical environment.Moreover, there are several advantages of OSLDs over other types of dosimeters, including high sensitivity, reproducibility, and tissue equivalence (Reft 2009, Dunn et al 2013, Hoshida et al 2019).They are also re-usable, easy-to-implement (Liu 2020) and relatively cost-effective, i.e. good candidates for dosimetry QA checks, remote dosimetry and audit tests (Jahn et al 2014, Lye et al 2014, Hoshida et al 2019, Kido et al 2023).
However, accurate QA procedures with OSLDs require accounting for dose-response characteristics and dependencies.Studies have reported angular dependence (also referred to as detector orientation dependence) of OSLD response with respect to the incident beam ranging from ∼2% to 4% (Kerns et al 2011, Lehmann et al 2014).The effect is influenced by several factors, including the design of the dosimeter, as well as the type and energy of radiation (Kerns et al 2011, Lehmann et al 2014).Additionally, temporal response correction may also be needed due to signal fading with time after irradiation (Kry et al 2020).The latter may be considerable especially in remote dosimetry or external audit tests.The dose-response calibration curve may deviate from linearity for high doses per fraction which are relevant in hypo-fractionated or stereotactic radiotherapy applications (Kry et al 2020).
Hybrid magnetic resonance-(MR-) Linac systems have been introduced in clinical practice as a new treatment modality.The Unity system (Elekta, Crawley, UK) combines a Philips 1.5T MR scanner (Philips Healthcare, Best, The Netherlands) with a 7 MV Agility-based linac head (Elekta, Crawley, UK) (Woodings et al 2018).More specifically, the linac is equipped with a Multi Leaf Collimator (MLC) (160 leaves with an effective field width of 7.175 mm (Roberts et al 2021)) delivering flattening filter free (FFF) step n shoot intensity modulated radiation therapy (IMRT) photon beams at a fixed energy of 7 MV.The beam is partly flattened as it passes through the helium cryostat and MR body coil, but these components also serve as sources of scatter radiation (Woodings et al 2018, Roberts et al 2021).The maximum field size is 57.4 × 22 cm 2 .The gantry rotates around the isocenter at a fixed source to axis distance (SAD) of 143.5 cm.The 1.5T static magnetic field is oriented parallel to the treatment couch and always perpendicular to the primary photon fluence.Due to the Lorentz force which affects the trajectory of the secondary electrons, challenges in MR-Linac dosimetry have been identified.In specific, dose-response of radiation detectors is affected by the presence of the 1.5T magnetic field at a degree which is both detector-and orientation-specific (O'Brien et al 2016, De Pooter et al 2021).Therefore, dosimetry formalisms have been adapted to include an additional magnetic field correction factor, k , B Q , to account for this effect (Malkov and Rogers 2018, Van Asselen et al 2018, De Pooter et al 2021).Furthermore, if plastic phantoms are used, the presence of small air gaps between the detector and phantom's walls may also affect the response, an effect which is more prominent in the case of asymmetrical air gaps (O'Brien andSawakuchi 2017, Margaroni et al 2023).
As for other passive dosimeters with no electrodes, such as films, thermoluminescence dosimeters (TLDs), radioluminescent glass detectors and alanine dosimeters (Kadoya et al 2012, Billas et al 2019, Billas et al 2020, Kry et al 2020), OSLDs may be good candidates for QA checks in beam gating or in vivo dosimetry applications involving real-time MR imaging during irradiation in MR-Linacs, due to the lack of ferromagnetic materials and their small sensitive volume.However, the OSLDs' dose-response dependencies and relevant effects should be well-characterized in the presence of a 1.5T magnetic field.In addition, the effect of radiofrequency (RF) and gradient magnetic fields (applied for MR image acquisition) on OSLD response (e.g. by heating up the housing case or the sensitive volume) have not been studied yet.Furthermore, two sub-millimeter air gaps are present between the active volume and the housing plastic case, which may affect dose-response characteristics and particularly the magnitude of angular dependence (Kerns et al 2011, Ito et al 2020, Tyagi et al 2022).A recent study showed that the static magnetic field can cause OSLD response changes around 1.3%/T (Spindeldreier et al 2017).
The scope of the present study is to investigate the dose-response characteristics and dependencies of OSLDs for dosimetry procedures in radiotherapy applications, mainly focusing on 1.5T MR-Linacs.To differentiate between MR-related and other dependencies, both conventional linacs and MR-Linacs are used.This work aims to determine which dependencies need to be corrected/accounted for and which effects can be considered negligible under specific conditions.Experimental dosimetry procedures were designed and carried out to quantify the relevant effects.In addition, Monte Carlo (MC) simulations were performed to study the OSLD's angular dependence in the presence of a 1.5T magnetic field, as well as to determine the corresponding k B Q , magnetic field correction factors for QA procedures employing OSL dosimetry.

Dosimetry formalism
In a conventional linac (i.e. in absence of a magnetic field) and according to AAPM TG-191 report (Kry et al 2020), the absorbed dose to water D , w by the clinical beam quality, Q, is determined by: where M corr is the corrected OSLD signal (see section 2.3), N D w , is the detector's calibration coefficient, k F is the fading correction factor for the signal decrease that occurs between irradiation and reading time, k L is the linearity correction factor for sensitivity changes with delivered dose, k Q is the beam quality correction factor, and k q is the angular correction factor accounting for response changes due to the detector orientation with respect to the incident beam.
If D w is measured in the presence of a static magnetic field, B, (i.e. in an MR-Linac), an additional correction factor, k , , is introduced to account for the effects related to the magnetic field (Van Asselen et al 2018).As a result, the absorbed dose to water, D , w B in the presence of a magnetic field, B, is determined by: where k B Q , is defined as the ratio of calibration coefficients with and without the magnetic field, i.e. (Van Asselen et al 2018):

=
Under the clinical beam quality, Q, and assuming that the detector's response is proportional to the absorbed dose to its active volume (OSLD supralinearity effects are accounted for by k

=
where D Q det, and D Q B det, are the absorbed dose to the detector's sensitive volume without and with the presence of magnetic field B, respectively.Equation (4) was used in the MC study of this work to determine k B Q , for OSLDs under different irradiation conditions (section 2.4.3).
This formalism and notation on the magnetic field correction factor are consistent with the International Atomic Energy Agency (IAEA) TRS-398 code-of-practice (Andreo et al 2000).Regarding the more recent IAEA TRS-483 code-of-practice (Palmans et al 2017), a different notation is used, and (Cervantes et al 2020(Cervantes et al , 2021 ) ).Despite the different notations, both factors are identical as they represent the same quantity, and can be determined by MC simulations using equation (4) (Cervantes et al 2020, 2021, Margaroni et al 2023).Hereinafter, the simpler notation, k , , is adopted for text clarity and conciseness.

OSL dosimeters
The commercially available nanoDot TM OSLDs (Landauer Inc., Glenwood, IL, USA) were used throughout this study.Their sensitive (active) volume, which is a disk (5 mm in diameter, 0.2 mm thick, ρ = 1.41 g cm −3 (Ito et al 2020)) made of aluminum oxide doped with carbon (Al 2 O 3 :C), is enclosed in-between two thin layers (films) of polyester (ρ = 1.03 g cm −3 ).Geometric details and material compositions can be found in the literature (Kerns For the purposes of section 2.3 (i.e.experimental measurements of this work), the OSLDs were read-out by a dedicated microSTAR TM ii reader (Landauer Inc., Glenwood, IL, USA), following the vendor's recommendations for handling, storage, and read-out.Signal acquisition and database registration were carried out using the accompanying microSTAR ii dosimetry software version 1.0.5018(Landauer Inc., Glenwood, IL, USA).Prior to every irradiation, OSLD bleaching (i.e.signal erasing) (Kry et al 2020) was carried out by a custom device incorporating an LED lamp (model IBRS 10461 by Philips lighting, specifications: 12.5 V, 1521 lm, 4000 K) and a protective box.The purpose of the latter was to house the dosimeters and prevent dust accumulation during bleaching.Typical light source to dosimeters distance was 6 cm.Bleaching duration was set to 24 h to ensure complete signal erasing, for any dose delivered, relevant to this study.This was also verified during read-out of the erased dosimeters in order to determine the new background signal.

Experimental study
A 30 × 30 × 1 cm 3 slab phantom made of RW3 (PTW, Freiburg, Germany) (ρ = 1.045 g cm −3 (Hill et al 2008)) was machined to accommodate the nanoDots in all three cardinal orientations, as shown in figure 1(b); (i) the 'coronal' orientation in which the detector's plane coincides with the slab phantom's plane and is perpendicular to the beam at gantry angle 0 o , and (ii) the 'axial' orientation in which the detector's plane is perpendicular to the slab phantom and parallel to the primary photon field (at gantry angle 0 o ).Furthermore, rotating the slab phantom by 90 o allows for (iii) the 'sagittal' orientation if the detectors are placed perpendicularly to the slab (figure 1(b)).
The experimental measurements were carried out in a conventional linac, as well as in a 1.5T MR-Linac (figure 1).Regarding the former, a VersaHD linear accelerator (Elekta, Crawley, UK) was used.Flattened 10 × 10 cm 2 photon fields were delivered to the detectors at an SAD = 100 cm (figure 1(c)).Dose delivery in the presence of 1.5T magnetic field was performed in a Unity 1.5T/7 MV MR-Linac system (Elekta, Crawley, UK) (figure 1(d)).Its key characteristics were described in section 1.In both delivery systems, a calibrated ion chamber was always used to verify the delivered dose and constancy in linac output.
In all experimental investigations, each detector was placed in the central socket of the phantom for the corresponding orientation, and its active volume was centered at the linac's isocenter (SAD = 100 cm for the conventional linac and SAD = 143.5 cm for the MR-Linac).Additional RW3 slabs were used in order for the detector to be located at a depth of 5 cm.Since the tabletop-to-isocenter distance in Unity is fixed at 14 cm, the total thickness of the slab phantom reached 19 cm.The same total thickness and detector depth were considered in both treatment delivery systems for consistency.In all irradiations, a 10 × 10 cm 2 field was used centered around the detector.
For the purposes of the present study, a total of sixty nanoDots were employed which were regarded as a single batch, implementing the relevant recommendations in AAPM TG-191 (Kry et al 2020).OSLD bleaching was performed before any experimental procedure or calibration step, which erased the dosimeters and yielded a negligible background signal (10-20 counts as compared to a signal of 10 4 counts per Gy of delivered dose).The element sensitivity factor, k , s i , for each detector i, was independently determined by the authors, according to the 'High Accuracy' dosimetric protocol (Kry et al 2020).k s i , is defined as the ratio of the individual dosimeter's response to a predetermined uniform dose, M , i to the mean response to the same dose from all the detectors in the same batch, ̅ M, i.e.: More specifically, for k s i , correction factor determination, using a conventional 6 MV linac and a 10 × 10 cm 2 field with a TPR 20,10 of 0.676, a uniform dose of 100 cGy was delivered to all OSLDs and each detector was read twice, i.e.M i in equation ( 5) was determined as the mean raw signal from two read-outs.In all experimental procedures, each detector was also read-out two times and the mean raw signal, M i raw, was calculated (Kry et al 2020).Then, the corrected signal from each detector, M , i corr, was obtained according to the protocol by Kry et al (2020): , raw,

=
In order to account for signal depletion after the first read-out, a signal depletion factor, k , d of 0.03% per read-out was applied to each successive read-out for doses above 20 cGy (Dunn et al 2013, Kry et al 2020).Although this correction can be considered negligible in most studies, for signal fading determination, each detector was read-out several times and therefore considerable depletion may occur.
By using equations ( 5) and (6) to determine the corrected OSLD response in a dosimetry procedure, it is assumed that the background signal, M , bkg is negligible.This is a common approximation made in clinical practice for radiotherapy applications (Kry et al 2020).Due to OSLD bleaching preceding all irradiations, background signal was typically between 10 and 20 counts and, thus, can be safely disregarded compared to the raw signal which is of the order of 10 4 counts Gy −1 .
Hereinafter, the corrected signal, M , corr obtained using equations ( 5) and (6) will be directly referred to as 'response', for increased text clarity and conciseness.

Dose-response linearity
The OSLD response to a range of delivered doses from 100 to 1000 cGy was studied in the case of axial orientation and a 6 MV photon beam.Three OSLDs were irradiated to each dose level and the mean response was determined.In addition, dose-response linearity was independently studied in the presence of a 1.5T magnetic field, i.e. the Unity 1.5T MR-Linac, using the same orientation.More specifically, the measurements were repeated in Unity using the 7 MV 10 × 10 cm 2 photon field with delivered doses reaching 800 cGy.In all cases, the corresponding data were used to derive the dose-response calibration curves from each dataset.To always ensure that the dosimeter is placed at the isocenter (given the unflattened field of Unity), all OSLDs were irradiated one-by-one, i.e.only one OSLD was loaded to the phantom per irradiation, in both treatment modalities.Linearity was assessed (without and with the presence of a 1.5T magnetic field) by applying a 1st order polynomial fit to each dataset.

Signal fading
The temporal fading of the OSLD signal as a function of time after the irradiation was quantified in groups of five OSLDs in a conventional linac.All dosimeters were irradiated at the dose of 100 cGy.Each dosimeter was read on day 3, 9 , 15, 20 and 30 after irradiation.To investigate whether fading rate depends on irradiation conditions, additional measurements were designed and carried out in the same linac.More specifically, the OSLD signal fading rate was compared for (i) beam qualities 6 MV and 10 MV, (ii) coronal and axial detector orientations, and (iii) dose rates of 144, 292 and 590 MUs min −1 .In all cases, the OSLD response was normalized to the third day after irradiation.All measurements were based on the mean response from three OSLDs.

OSLD response dependencies in a conventional linac
In an effort to investigate OSLD response dependencies in a conventional linac set-up, OSLD response was compared for two photon beam energies (6 and 10 MV), two cardinal orientations (coronal and axial) and three dose rates (144, 292 and 590 MUs min −1 ).All measurements were conducted in groups of three OSLDs and the mean response from each group was assessed.In order to be consistent however, only one detector was loaded to the slab phantom per irradiation and centered at the linac's isocenter.

MR imaging related OSLD response dependencies
In the Unity MR-Linac system, the effect of gradient magnetic fields and RF fields on OSLD response was additionally quantified.For this purpose, real-time T2-weighted (T2w) imaging was enabled during phantom irradiation with detectors placed at both the axial and coronal orientations (one detector placed per irradiation).Irradiations were repeated without real-time imaging for comparison.This study aimed to investigate whether MR imaging can affect OSLD response, and thus whether these detectors are suitable for beam gating QA checks or in vivo dosimetry in MR-Linacs.

Monte Carlo study 2.4.1. Source model and simulated geometry
In addition to experimental measurements, computational dosimetry using the EGSnrc V2019 MC code package (Kawrakow et al 2013) was used to further study the OSLD angular dependence and to calculate the k B Q , correction factors for various orientations, according to equation (4), in the presence of a 1.5T magnetic field.As a source model, the phase space file for the 10 × 10 cm 2 field was provided by the MR-Linac manufacturer following a non-disclosure agreement.The same source model and MC code were also used in our previous study on MR-Linac dosimetry (Margaroni et al 2023).
The nanoDot OSLD was modelled according to the geometrical characteristics taken from the literature (Kerns et al 2011, Ito et al 2020) and the blueprints provided by the manufacturer (Landauer Inc., Glenwood, IL, USA).All components including the active volume, film layers, air gaps and the external plastic case were modelled in-detail (figure 2 and section 2.2).Simulated detector geometries in all three cardinal orientations with respect to the magnetic field and primary photon fluence are shown in figure 2. All materials involved were simulated using the PEGS4 code (Kawrakow et al 2013) with parameters related to the density effect adopted from NIST (Berger et al 2005).

Angular dependence in an MR-linac
Angular dependence in the presence of a 1.5T magnetic field was studied for the coronal and axial detector orientations (in accordance with section 2.3.3 in a conventional linac).For this purpose, an OSL dosimeter was simulated at a depth of 5 cm inside a slab phantom made of RW3 (external dimensions 30 × 30 × 19 cm 3 , mass density of 1.045 g cm −3 (Hill et al 2008)), as in the experimental study.The source-to-surface distance (SSD) was set to 138.5 cm in order for the OSLD's sensitive volume to be at SAD = 143.5 cm.Moreover, the effect was also quantified at other non-cardinal angles.More specifically, for both cardinal orientations, calculations were repeated after rotating the detector around its central axis being parallel to the magnetic field (i.e. the y-axis in figure 2) with a step of 45 o .Selecting y-axis as the axis of rotation under investigation was based on the fact that this is the only degree of freedom for the gantry in Unity, and thus simulating different incident beam angles.It is noted that if a rotation of 90 o around the y-axis is applied to the cardinal coronal orientation, the cardinal sagittal orientation is reproduced (figure 2).In all simulations, gantry angle was always fixed at 0 o , as shown in figure 2, resulting to a primary photon fluence on the z-axis and the Lorentz force on the x-axis.

k B Q
, determination The computational framework and steps for k B Q , determination have been described in our previous publication (Margaroni et al 2023).Gantry angle was simulated at 0 o and k B Q , was determined for all three cardinal orientations: (i) axial, (ii) coronal and (iii) sagittal (figure 2).Given that the OSL detector is not exactly symmetrical in all directions and to cover all possible orientations, calculations were repeated with the OSL dosimeter rotated by +90 o and −90 o around the y-axis (the positive rotational direction is depicted in figure 2).2.4.4.Simulation parameters All simulations were carried out using the egs_chamber user code (Wulff et al 2008), incorporated in the EGSnrc installation package.Total electron energy cutoff threshold (ECUT) and photon energy cutoff threshold (PCUT) were set equal to 512 keV and 1 keV, respectively.All other EGSnrc transport parameters and cross-sectional options were set to their default values.In order to improve MC simulation efficiency, Russian Roulette, and photon-cross section enhancement (XCSE) variance reduction techniques were enabled (Wulff et al 2008).An XCSE factor of 512 was applied to all geometry regions located within a box of 2 × 2 × 2 cm 3 centered at the scoring regions (Pappas et al 2016).For the simulations requiring the presence of a 1.5T magnetic field, the electromagnetic field macros (EEMF_macros.mortran)was enabled (Malkov and Rogers 2016), applying a uniform magnetic field in the entire geometry, anti-parallel to the y-axis, as shown in figure 2. According to the Fano cavity test in the presence of a 1.5T magnetic field, conducted by our group for the same algorithm and MC code version, simulation accuracy is 0.13% or better (Margaroni et al 2023).All simulations were performed by the ARIS high-performance computer (GRNET-National Infrastructures for Research and Technology), consisting of 426 computational nodes with 10 Ivy Bridge Intel Xeon E5 v2 processors per node, which offered a total of 8520 CPU (computational threads), clocked at 2.8 GHz.The number of initial particle histories varied in order to achieve combined Type A (statistical) uncertainties below 0.1% for k B Q , determination.

Uncertainty budget
Table 1 lists the uncertainty contributors for both the experimental and MC studies.Wherever available, uncertainty levels were adopted from relevant publications as best estimates.As an instance, there are no data on detector geometry variations for OSLDs.However, an uncertainty of 0.26% is considered, as determined in the study of Cervantes et al (2020) for ionization chambers, as being the best estimate available.The uncertainty related to OSLD read-out reproducibility was adopted from the literature (Mrčela et al 2011, Alves et al 2015) for microSTAR i, but it is also reader-dependent and no data for microSTAR ii could be found.OSLD reader characterization was beyond the scope of this work.
It is noted that throughout this study, relative detector responses are being compared, i.e. absolute dose determination was not performed.Thus, in most cases, systematic errors are not relevant (cancelled out due to normalization).In section 3, Type B (systematic) uncertainties are only reported in the case presented results are uncorrelated.When comparing correlated results, Type A (statistical) uncertainties are only considered, while the combined total (Type A + B) uncertainty is associated with uncorrelated results under evaluation.

Results
3.1.Experimental study 3.1.1.Dose-response linearity For the same irradiation set-up (except for the SAD) in a conventional 6 MV linac and a 1.5T/7 MV MR-linac, OSL dose-response is presented in figure 3(a).Although the datapoints appear to follow a linear trend, the response does not increase proportionally with delivered dose, i.e. supralinearity is observed for doses above 2 Gy.This becomes more obvious in figure 2(b), where the response per dose (sensitivity) is presented for each datapoint, normalized to the sensitivity at 1 Gy.These results are consistent with the literature on OSLD supralinearity in conventional linacs (Reft 2009, Kry et al 2020).More importantly, OSL dose-response supralinearity is not affected by the presence of the 1.5T magnetic field, or the difference in beam qualities (6 MV versus 7 MV), at least for the range of doses shown in figure 3 and the axial detector orientation.By applying equations (1) and (2), this remark also implies that the k B Q , correction factor for the axial orientation can be considered unity (see also section 3.2.2).

Signal fading
Following irradiation in a conventional 6 MV linac, the OSLD signal fading as a function of time is shown in figure 4. Results have been normalized to the signal measured on day 3.By performing a 1st order polynomial fit, a signal reduction of (0.19 ± 0.05)%/day was determined, at least for the period of 3-30 d covered in this study.
In order to reveal any potential dependence of signal fading rate on irradiation parameters, measurements were repeated under different beam qualities, detector orientations, dose rates and dose levels.Fading rates (in %/day) are presented in figure 5, after a 1st order polynomial fit, covering a period of 3-30 d after irradiation, in accordance to figure 4. a k s i , is calculated according to equation (5).The corresponding uncertainty, however, resulted only from the uncertainty in M .
i The standard deviation of the mean signal from the entire batch, ̅ M, was not propagated as uncertainty in k , s i , because only relative responses are compared throughout this experimental study, and, consequently, all results are correlated in terms of ̅ M. For direct dose determination using equations (1) and (6) (not performed herein), an additional uncertainty of 3.5% in k s i , (at the 68% confidence level) should be considered, according to the present study results.b MC uncertainty due to detector geometry variations for nanoDots has not been specified.The corresponding uncertainty for ionization chambers was adopted from the literature as the best estimate available.

Dependencies in a conventional linac
In figure 6, OSLD response dependencies are investigated in the absence of a magnetic field (i.e. in a conventional linac).According to the presented results, differences between the measured OSLD responses in 6 and 10 MV fields are insignificant, taking into account the relevant experimental uncertainties (figure 6(a)).Detector orientation (coronal versus axial) affects OSLD response (figure 6(b)), suggesting that any relevant correction factors adopted in a dosimetry protocol should be orientation dependent.Furthermore, there is no dose rate dependence for the dose rates investigated (figure 6(c)).

MR imaging-related dependencies
Figure 7 focuses on potential response dependencies related to the RF and gradient magnetic fields emitted during MR image acquisition.OSLD response if irradiated under real-time T2w imaging is evaluated and  compared against the response obtained without T2w imaging enabled but under the same irradiation conditions and set-up.
A deviation of 9.2% in OSLD response was revealed when comparing axial with the coronal detector orientations (figure 7).Real-time T2w imaging during irradiation does not appear to affect OSLD response  (figure 7) for both orientations considered, suggesting that OSLDs are suitable for use in relevant MRI-based beam gating QA procedures or in vivo dosimetry in an MR-Linac.

Angular dependence
Results of the MC simulations performed to investigate the angular dependence of OSLD response in an MR-Linac are shown in figure 8. Placing the detector in the axial orientation and rotating it around its central y-axis, which is parallel to the magnetic field, does not affect the dose scored in its active volume.However, if the detector is placed in the coronal orientation and rotated around the same axis, deviations of up to 4.6% were detected (figure 8).

k B Q
, correction factors Using equation (4), k B Q , correction factors for all three cardinal detector orientations are given in table 2. In addition, k B Q , values after rotating the detector by +90 o and −90 o around its central y-axis, which is parallel to the magnetic field, are also given.According to table 2, k B Q , values are strongly orientation dependent, with corrections needed ranging from (0.3 ± 0.4)% up to (6.4 ± 0.4)%.It is noted, however, that if the OSLD is placed in the axial orientation, then k B Q , = 1 within uncertainties, irrespective of the rotation around the magnetic field.This remark on k B Q , value is in accordance with the results shown in figure 8 on angular dependence.

Discussion
In the absence of a strong magnetic field, OSL dosimetry has been evaluated in several studies (Jursinic 2007, Jursinic 2010, Mrčela et al 2011, Omotayo et al 2012, Reft 2009, 2012, Dunn et al 2013, Lehmann et al 2014), with the available data summarized in AAPM TG-191 (Kry et al 2020).A supralinear dose-response behavior has been reported for doses above ∼2 Gy, reaching approximately 15% at the dose level of 10 Gy (Jursinic 2010, Mrčela et al 2011, Omotayo et al 2012).Moreover, it has been shown that dose-response also depends on the bleaching time, bleaching wavelength, and accumulated dose (Omotayo et al 2012).Results of the present study confirm OSLD supralinearity, supporting the need to apply linearity correction factors, k , L as suggested in the relevant dosimetry protocol (Kry et al 2020).The data shown in figure 3(b) can serve as 1/k L values for nanoDots, provided that the OSLD standards in an experimental procedure have been irradiated at the dose level of 1 Gy, i.e.N D w , has been determined at 1 Gy (Kry et al 2020).More importantly, according to figure 3, the OSLD sensitivity is not affected by the presence of a 1.5T magnetic field, nor the change in beam quality from 6 to 7 MV, at least within uncertainties.Thus, for the range of doses investigated and the axial detector orientation, k L values (or N D w , ) determined in a conventional 6 MV linac can be safely applied to a 1.5T/7 MV MR-Linac.Table 2 also provides MC-based data in support of the latter remark regarding the axial orientation.Spindeldreier et al (2017) reported an OSLD response difference of 1.3%/T.In addition to studying a different OSLD type with unknown air gaps, the authors investigated the coronal detector orientation and thus results are not directly comparable.After a wait time of at least 10 min, OSLDs can be read-out any time or day after irradiation (Kry et al 2020).However, signal fading is expected and should be considered if read-out time for the calibration and experimental detectors are not matched.For the range of 3-30 d, a fading rate of (0.19 ± 0.05)%/day was obtained in this study, after applying a 1st order polynomial fit.Our results are in agreement with published data (Kry et al 2020), although we have only focused in the time-scale of days.If minutes or hours after irradiation are considered for read-out, a more complex behavior is expected (Reft 2009, Mrčela et al 2011, Butson et al 2017), and the rate of 0.19%/day does not apply.
Another important finding of the present study is that, in a conventional linac, the fading rate is not affected by the irradiation conditions, such as beam quality, detector orientation, delivered dose, and dose rate (figure 5).Consequently, a fading correction factor, k F (see equations (1), (2) and AAPM TG-191 (Kry et al 2020)), determined in-house under specific irradiation conditions or adopted from the literature can be safely applied to account for signal fading in a dosimetry QA check.
OSLD responses in 6 and 10 MV fields did not differ significantly, taking into account the related experimental uncertainties (figure 6(a)).Energy dependence has also been studied in the literature with consistent findings.More specifically, no energy dependence has been reported for the clinical megavoltage photon fields up to 18 MV (Jursinic 2007, Reft 2009, 2012).Consequently, the corresponding beam quality correction factor, k , Q can be considered unity in this energy range.In support of the latter, according to the Table 2. MC-based k B Q , correction factors for the three OSLD cardinal orientations as well as after rotating the detector by +90 o and −90 o around its central y-axis being parallel to the magnetic field (positive rotational direction is depicted in figure 2).Reported uncertainties correspond to the combined total MC uncertainties (Type A+B) at the 68% confidence level.results shown in figure 3 the effect of energy dependence between a 6 MV flattened field and a 7 MV unflattened field can be considered negligible for the axial detector orientation.OSLD response in a conventional 6 MV linac is expected to drop by 2%-4% if the detector is irradiated edgeon compared to en face (Kerns et al 2011, Lehmann et al 2014).In the present study, an angular dependence correction factor, k q (see equations (1), ( 2) and AAPM TG-191 (Kry et al 2020)), of 0.967 was determined after comparing OSLD responses irradiated in the coronal and axial orientations (figure 6(b)).Our experimental results are in good agreement with published data in the absence of a strong magnetic field (Kerns et al 2011, Lehmann et al 2014).
In an MR-Linac setting, however, the angular dependence effect is more pronounced as demonstrated in both experimental and MC studies of this work.In the presence of a 1.5T magnetic field, OSLD response dropped by 9.5% when an axial orientation was considered, as compared to the coronal orientation (figure 7).Thus, the impact is more than doubled in MR-Linacs due to the presence of the magnetic field and the air gaps above and below the active volume.Therefore, the corresponding angular dependence correction factor, k , q should be determined specifically in an MR-Linac setting.Alternatively, if OSLDs calibration has been performed in the axial orientation (e.g. in a conventional linac), then k q can be considered unity for all angles of incident beams in an MR-Linac dosimetry check, provided that the detector has been also placed in the axial orientation (figure 8).
Interestingly, OSLD response is not affected by the RF and gradient magnetic fields emitted during real-time T2w image acquisition.This is evident from figure 7 for both axial and coronal orientations.To the best of our knowledge, this is the first study to investigate potential OSLD response changes due to the non-static magnetic fields and RF fields, associated with potential heating of the OSLD or other microscopic effects.According to the presented results, OSLDs are suitable for QA checks in MR-based beam gating applications and in vivo dosimetry in MR-Linacs.
MC calculations were performed to determine the last correction factor in equation (2), introduced to specifically account for the change in OSLD response due to the presence of a 1.5T magnetic field, i.e. k .

B Q
, Table 2 summarizes the obtained results for all three cardinal orientations, as well as after applying a rotation of +90 o and −90 o around the y-axis.k B Q , values strongly depend on orientation.Corrections needed reached up to 6.4%.However, if OSLDs are calibrated in the axial orientation and then irradiated in an MR-Linac placed again in the axial orientation (perpendicular to the magnetic field), then k B Q , is unity within uncertainties, irrespective of the incident beam angle, given that the gantry can rotate only around the y-axis.Thus, for dosimetry QA checks involving several gantry angles, MC results suggest that the OSL detector is placed in the axial orientation.
A limitation of the present study is that a specific OSLD type and model was assessed.Given the differences in active volume material, dimensions, air gaps, handling, and bleaching protocols with other commercially available OSLDs (Jahn et al 2014), results presented herein can be considered applicable only to nanoDots.Future studies should focus on the effects on other OSLD types and models.Moreover, the Unity system was investigated, although MR-induced effects are also expected in MR-Linacs comprising lower magnetic field strengths (Spindeldreier et al 2017).OSLD reader characterization was outside the scope of this study, and relevant effects were disregarded.However, drifting of the reader over a period of several months has been demonstrated (Dunn et al 2013), and therefore N D w , re-determination is recommended by irradiating standards to a reference dose for every dosimetry procedure (Kry et al 2020).This approach was followed in addition to the fact this study did not involve data acquisition over a long period of time.Effort was made to ensure that all OSLDs had the same irradiation and bleaching history to avoid relevant signal regeneration effects (Liu 2020).In the MC study of this work, a phase space source model was used provided by the MR-Linac manufacturer.An independent source model validation was not performed by the authors, although results were consistent with experimental measurements.Furthermore, the same source model was used in our previous study and results were validated against published experimental studies (Margaroni et al 2023).Lastly, MC methods cannot account for intrinsic OSLD response dependencies, such as response supra-linearity or potential dose rate dependencies (if any).Thus, experimental measurements are warranted to complement MC findings.
As passive dosimeters with high sensitivity, OSLDs are promising detectors for dosimetry QA checks, endto-end tests, remote audits, surface dose determination, and in vivo dosimetry (Dunn et al 2013, Lye et al 2014, Zhuang and Olch 2014, Alves et al 2015, Zakjevskii et al 2016, Ponmalar et al 2018).However, a large number of dependencies has been identified (Kry et al 2020), suggesting that calibration, irradiation, read-out and handling parameters need to be carefully controlled for high-fidelity dosimetry.In MR-Linacs, the presence of a 1.5T magnetic field adds more concerns, challenges, and uncertainties.More studies are needed to fully characterize the OSLD response, associated dependencies, and underlying effects.Given that all dependencies are detectortype dependent, and some are also reader-specific, future publications should focus on other OSLD systems for which the literature is even more limited.

Conclusion
OSLD response and relevant dependencies were evaluated in a conventional linac and a 1.5T MR-Linac (i.e. with and without the presence of a strong magnetic field).Both experimental and MC methods were employed.Effort was made to quantify the dependencies identified in the AAPM TG-191 dosimetry formalism, in addition to the ones induced by the presence of the strong magnetic field in MR-Linacs.
This study confirms supralinearity in OSLD dose-response for doses above 2 Gy.The same effect and of the same magnitude (within uncertainties) was observed for MR-Linacs with the detector positioned in the axial orientation.This implies that OSLD dose-response is not considerably affected by the presence of the magnetic field or the difference in beam quality (6 MV versus 7 MV), and consequently, linearity correction factors, k , L determined in 6 MV conventional linacs can be safely applied in 1.5T/7 MV MR-Linac dosimetry applications, provided that the detector is placed in the axial orientation in both set-ups.
In a conventional linac, a signal fading rate of (0.19 ± 0.05)%/day valid in the range of 3-30 d post irradiation was determined after applying a 1st order polynomial fit.This rate is not affected by the irradiation conditions such as beam quality, dose rate, detector orientation and dose levels.Fading correction factors, k , F determined under different irradiation conditions or adopted from the literature can be safely applied in a dosimetry QA check irrespective of the irradiation conditions.
In a conventional linac, OSLD response was not found to significantly depend on beam quality (6 MV versus 10 MV).However, orientation dependence was confirmed; a difference of 3.3% in OSLD response between the axial and coronal orientations was observed.At least in the range considered, OSLD response is independent to the dose rate.
In an MR-Linac however, the angular dependence was found considerably enhanced, reaching 9%.Thus, an angular correction factor, k , q determined in a conventional linac does not necessarily apply in a dosimetry protocol for MR-Linacs.
OSLD response is not affected by MR imaging-related fields applied during irradiation.In specific, OSLDs irradiated with and without real-time T2w MR imaging enabled during irradiation yielded the same response within uncertainties.This remark enables OSL dosimetry for beam gating QA checks and in vivo dosimetry in MR-Linacs.
Magnetic field correction factors, k , B Q , were determined for all three cardinal orientations.Corrections needed reached up to 6.4%.However, if OSLDs are calibrated in the axial orientation and then irradiated in an MR-Linac placed again in the axial orientation (perpendicular to the magnetic field), then k B Q , factors were found unity within uncertainties, irrespective of the angle with the incident beam.Given that the gantry can rotate only around the y-axis, for dosimetry QA checks involving several gantry angles, results of this study suggest OSLDs to be placed in the axial orientation.
This work contributes towards OSLD response characterization and relevant data availability, with emphasis on MR-Linac dosimetry.However, the presented results are applicable only to the nanoDots OSLDs and the 1.5T MR-Linac.

ORCID iDs
Pantelis Karaiskos https:/ /orcid.org/0000-0002-3665-2989Eleftherios P Pappas https://orcid.org/0000-0003-4030-2241 al 2011, Ito et al 2020).The disk is housed in a protective case with external dimensions of 10 × 10 × 2 mm 3 , as shown in figure 1(a).According to the blueprints provided by the manufacturer and relevant published articles (Kerns et al 2011, Ito et al 2020), sub-millimeter air gaps of 0.4 mm are inevitably introduced above and below the disk.Moreover, the centroid of the active volume (reference point of measurement) is indicated by a relevant mark on the housing case and is shifted by 1 mm with respect to the geometrical centroid of the detector (figure 1(a)).

Figure 1 .
Figure 1.(a) Four samples of the nanoDots OSLDs (Landauer, Inc., Glenwood, IL, USA) used throughout this study.The active volume based on Al 2 O 3 :C is shown in the first one.(b) The 30 × 30 × 1 cm 3 slab made of RW3 (PTW, Freiburg, Germany) was machined to accommodate OSLDs in two orientations.(c) The slab phantom with two OSLDs placed in two orientations in a conventional linac (VersaHD, Elekta, Crawley, UK), for demonstration purposes.(d) As in (c) but in a Unity 1.5T/7 MV MR-Linac (Elekta, Crawley, UK).

Figure 2 .
Figure 2. The three OSLD cardinal orientations in an MR-linac with gantry angle at 0 o .The yellow arrow indicates the positive rotation angles applied for the purposes of sections 2.4.2 and 2.4.3.Color legend; blue: OSLD case, Magenta: OSL chip, light blue: thin polyester film covering the chip, red: air gap around the OSL chip. B: magnetic field;  : F primary photon fluence;  F : Lorentz force for an electron with velocity parallel to  .F

Figure 3 .
Figure 3. (a) OSL dose-response data for a 6 MV Linac (blue color, up to 1000 cGy) and a 1.5T/7 MV MR-Linac (orange color, up to 800 cGy) with the detector placed in the axial orientation.(b) For each datapoint, the response per dose (sensitivity) is presented normalized to the sensitivity at 100 cGy.Dashed lines represent the ideal linear response (y = a * x) based on the response at the dose of 100 cGy.Error bars correspond to the combined total (Type A + B) experimental uncertainties, at the 68% confidence level.

Figure 4 .
Figure 4. OSLD signal fading after irradiation by a conventional 6 MV linac, using a 10 × 10 cm 2 irradiation field and a dose rate of 590 MU/min with the detector placed in the axial orientation.Data are normalized to the response measured on the third day.Error bars correspond to the Type A experimental uncertainties, at the 68% confidence level.The solid line represents a 1st order polynomial fit to the measured data.The dashed lines represent the upper and lower 95% prediction boundaries.

Figure 5 .
Figure 5. Investigation of OSLD signal fading rates under different irradiation parameters.Comparison between (a) 6 MV and 10 MV beam qualities, (b) coronal and axial detector orientations, (c) dose rates, and (d) dose levels.Error bars represent the 95% prediction bounds of the rate determined after a 1st order polynomial fit to the data measured for a period of up to 30 d.

Figure 6 .
Figure 6.Investigation of OSL response dependencies in a conventional linac.(a) Energy dependence, (b) orientation dependence, (c) dose rate dependence.The data are normalized to (a) the 6 MV photon beam, (b) coronal orientation and (c) 144 MU min −1 , respectively.In figure 6(a), error bars correspond to the combined total (Type A + B) experimental uncertainties at the 68% confidence level (i.e.linac output calibration uncertainty is included).In figures 6(b) and (c), error bars correspond to the Type A experimental uncertainties, at the 68% confidence level.

Figure 7 .
Figure 7. Investigation of potential MR imaging-related OSLD response dependencies.Comparison of the response obtained after irradiation in an MR-Linac with the detectors positioned in the coronal and axial orientations, with and without real-time T2w image acquisition during irradiation.All 4 datapoints are normalized to the response of the detector placed in the coronal orientation without T2w imaging.Error bars correspond to the Type A experimental uncertainties, at the 68% confidence level.

Figure 8 .
Figure 8. MC results regarding angular dependence of OSLD response for the coronal and axial orientations in a 1.5T/7 MV MR-Linac.All datapoints are derived after rotating the detector around its central axis which is always parallel to the magnetic field (i.e. the y-axis, figure 2).Gantry angle is always simulated at 0 o .The data have been normalized to the 0 o rotation angle which corresponds to the cardinal orientations shown in figure 2. Error bars represent Type A MC uncertainties, at the 68% confidence level.

Table 1 .
Uncertainty budget for both the experimental and MC studies.